Approximate series solutions of the output pulse waveforms and transmission efficiencies of transmission line with exponential impedance profile have been developed based on distributed-parameter model for typical incident pulses suitable for next generation of Z -pinch plasma drivers. The transmission efficiencies are studied computationally with these solutions for petawatt-class Z-pinch driver's exponential transmission line taking account of the line's length and ratio of output impedance to the input as well as the pulse's shape and parameter. The voltage transmission efficiency increases with the increase of the ratio of output impedance to the input, line length and pulse frequencies; the power transmission efficiency increases with the increase of pulse frequencies and with the decrease of steepness of the line's impedance variation.

It was demonstrated, based on the PSPICE circuit simulation, that the sectioning number for the circuit simulation of an exponential transmission line should be determined as twice the line's one-way electromagnetic wave transport time (electric length) divided by the wave-front of input pulse, owing to elimination of the wave reflections caused by artificial impedance discontinuity in the line's circuit simulation model, which employs a serial and sectional transmission line with impedances constant in each section but stair-step-varied between sections, and with total electric length the same as that of the exponential line under simulation. A pulse of 112.2 ns wave-front propagates through an exponential water transmission line of 1234.2 ns one-way transport time will give the best sectioning number of 22, when the constant impedance of each section is given by the geometric mean of the two ends' impedances of the corresponding section on the exponential line under simulation. This sectioning rule is equivalent to the statement that the two-way transport time of each section should be equal to the input pulse's wave-front.